Task 1: Calculate the dielectric constant

The dielectric constant describes the response of a system to an external electric field. Within a linear response approximation the Kubo Formula is applicable. The Kubo Formula is an equation which expresses the linear response of an observable quantity due to a time-dependent perturbation. Hence, one can calculate the dielectric constant based on a sampling of the dipole moment.

The advantage of Monte Carlo is that we can employ special hydrogen reordering moves, which lead to an effective sampling of the dipole.

Run the input-file mc_exercise.inp. It will create a file tmc_trajectory_T200.00.dip_cl, which contains the dipole moment for each accepted step. Plot the histogram of the z-component of the dipole moment. The distribution should be symmetric, because the simulation cell is also symmetric in the z-direction.

Task 2: Gather more samplings

You can gather more samples by launching multiple independent runs in parallel with different random number seeds. The seed is given by the RND_DETERMINISTIC keyword. The gathered trajectories can then be analyzed collectively with the python-script:

Task 3: Calculate the thermal expansion coefficient

Run the MC sampling again at temperature of 150K . Plot the cell volume of each sampling. Read off the converged cell volume and plot it vs. the temperature. Determine the expansion coefficient via a linear fit. Do you trust your result? Why (not)?